scattergood
n. a person who spends money wastefully
Built in the 16th century to flaunt its owner’s wealth, Hardwick Hall, in Derbyshire, boasted large windows when glass was a luxury. Children called it “Hardwick Hall, more glass than wall.”
Unfortunately, writes Stephen Eskilson in The Age of Glass (2018), “a cold day saw the chimneys of Hardwick Hall drawing cold air through the drafty windows and circulating it again to the outside,” “a sui generis example of thermal inefficiency.”
Here’s a depressing idea: In 1994, Italian physicist Cesare Marchetti suggested that people have always endured commutes of an hour a day, half an hour each way, on average. Improvements in urban planning and transportation haven’t shortened our travel time; they’ve just permitted us to live further afield. In 1934 Lewis Mumford had written:
Mr. Bertrand Russell has noted that each improvement in locomotion has increased the area over which people are compelled to move: so that a person who would have had to spend half an hour to walk to work a century ago must still spend half an hour to reach his destination, because the contrivance that would have enabled him to save time had he remained in his original situation now — by driving him to a more distant residential area — effectually cancels out the gain.
Marchetti attributed the idea to World Bank transportation analyst Yacov Zahavi. He found that the one-hour rule extends over the world and throughout the year; even the mean radius of villages in ancient Greece, he said, corresponds to this estimate, assuming a walking speed of 5 km/hr. As technology permitted greater speeds, cities grew correspondingly.
(Cesare Marchetti, “Anthropological Invariants in Travel Behavior,” Technological Forecasting and Social Change 47:1 [September 1994], 75-88.)
Here’s an oddity: In the figure on the right, a weight is suspended by two springs (AB and CD) connected by a short length of inelastic rope (BC). The blue curves are lengths of string, which are slack here.
Surprisingly, when the rope is cut, the weight rises (left). Why? In the initial state the springs were arranged “in series,” one above the other. When the rope is cut, the blue strings go taut, and now the two springs are arranged “in parallel,” working together and thus more effective in resisting the weight’s pull.
3 and 5 are “twin primes”: They’re two prime numbers that differ by 2. Further such pairs are 5 and 7, and 11 and 13. These pairs get sparser as you travel out the number line, but no one knows whether they eventually cease appearing altogether.
University of Alberta mathematician Leo Moser saw an opportunity in this pattern — if a prime magic square can be fashioned from the smaller partners in these pairs:
29 1061 179 227 269 137 1019 71 1049 101 239 107 149 197 59 1091
… then it immediately suggests a second prime square produced from the larger:
31 1063 181 229 271 139 1021 73 1051 103 241 109 151 199 61 1093
(“Strictly for Squares,” Recreational Mathematics Magazine 1:5 [October 1961].)
Draw a pentagram and enclose its arms in circles as shown. Each pair of adjoining circles will intersect at two points, one at a juncture of the pentagram’s arms. The second points of intersection will lie on a circle.
The converse is true if the centers of the five circles lie on that implied (red) circle (below): The lines connecting the second intersection points of neighboring circles will describe a pentagram whose outer vertices fall on the circles.
Discovered by Auguste Miquel.
Given names of the 11 children of Mr. and Mrs. Ernest Russell of Vinton, Ohio, 1972:
“Mother did it, but I don’t know why,” Laur told UPI. “She would take names from the Bible and other books and compare them until they came out that way.”
Bonus palindrome item: Volume 1, Issue 5 of Alan Moore’s graphic novel Watchmen, titled “Fearful Symmetry,” is a deliberately contrived visual palindrome, not just in structure but often within individual panels (designed by artist Dave Gibbons). Pedro Ribeiro shows the correspondences here.
[T]o the human mind there is more to blood than its mere chemical content. … For example, blood must essentially be thicker than water, impossible to get out of stones, indelible in its staining. … When apparent on heads, it should leave them unbowed; and should have the capacities to combine formidably with toil, tears and sweat and to attain boiling-point when its host faces frustration.
— Patrick Ryan, in New Scientist
An inquisitive ant sets out from point A at a bottom vertex of the 1 × 1 × 2 box shown above. Of all the possible destinations it might seek in a direct route along the surface of the box, which one requires the longest journey?
Intuitively we might think it’s point B, the farthest vertex on the box roof. But Japanese mathematician Yoshiyuki Kotani discovered that the longest journey actually ends one-fourth of the way along the rooftop diagonal that ends at point B.
This can be seen by “unfolding” the box into a flat diagram, where four different paths can be traced from A to that point. The Pythagorean theorem shows that all four paths have the same length, 2.850…, which is about 0.022 longer than the shortest path to B.
Data scientist Shiro Matsumoto provides some animations here.
(Martin Gardner, “The Ant on a 1 × 1 × 2,” Math Horizons 3:3 [February 1996], 8-9.)
Make an inverted triangle of hexagonal cells with side length 3n + 1, and color the cells in the top row randomly in three colors. Now color the cells in the second row according to these rules:
When you’ve finished the second row, continue through the succeeding ones, applying the same rules. Pleasingly, no matter how large the triangle, the color of the last cell can be predicted at the start: Just apply our two guiding rules to the endmost cells in the top row. If those two cells are both red, the last cell will be red. If one is red and one is yellow (as in the figure above), the bottom cell will be blue.
The principle was discovered by Newcastle University mathematician Steve Humble in 2012. Gary Antonick gives more background here, and see the paper below for a mathematical discussion by Humble and Ehrhard Behrends.
(Ehrhard Behrends and Steve Humble, “Triangle Mysteries,” Mathematical Intelligencer 35:2 [June 2013], 10-15.)
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