“It was hard for me to believe. I would look down and say, ‘This is the moon, this is the moon,’ and I would look up and say, ‘That’s the Earth, that’s the Earth,’ in my head. So it was science fiction to us even as we were doing it.” — Alan Bean, Apollo 12
The first “true cat,” Proailurus, or “Leman’s Dawn Cat,” appeared about 30 million years ago. But from 25 to 18.5 million years ago, strangely few catlike fossils are found in North America. Biologist Luke Hunter writes:
Following the appearance of the dawn cat, there is little in the fossil record for 10 million years to suggest that cats would prosper. In fact, although Proailurus persisted for at least 14 million years, there are so few felid fossils towards the end of the dawn cat’s reign that paleontologists refer to this as the ‘cat gap’. The turning point for cats came about with the appearance of a new genus of felids, Pseudaelurus.
The gap may be due to changes in climate and habitat, the rise of competing doglike species, an unsustainable “hypercarnivorous” dietary specialization, or some other factor. Modern cats descended from Pseudaelurus.
Three male offspring, aged 9–14 years, of one of the authors were observed to experience visual problems profound enough to imply functional blindness. The visual deficit was evident on almost every occasion when any one of the children of this physician went to the refrigerator and opened the door. The acute visual problem encountered was noted to be part of a consistent behaviour pattern, wherein a few seconds after the fridge door was opened a cry would be heard from the affected child of ‘Mum, where’s the milk?’
— Andrew J. Macnab and Mary Bennett, “Refrigerator Blindness: Selective Loss of Visual Acuity in Association With a Common Foraging Behaviour,” Canadian Medical Association Journal, Dec. 6, 2005
This is interesting: In 1585, Italian mathematician Giovanni Battista Benedetti devised a piece of music in which a precise application of the tuning mathematics causes the pitch to creep upward.
Avoiding this phenomenon requires an adjustment — a compromise to the dream of mathematically pure music.
Suppose that there’s no correlation between talent and attractiveness in the general population (left). A person who studies only celebrities might infer that the two traits are negatively correlated — that attractive people tend to lack talent and talented people tend to lack attractiveness (right). But this is deceiving: People who are neither attractive nor talented don’t typically become celebrities, and that large group of people aren’t represented in the sample. Celebrities tend to have one trait or the other but (unsurprisingly) rarely both.
The phenomenon was studied by Mayo Clinic statistician Joseph Berkson; this example is by CMG Lee.
In June 2006, Iowa paralegal Jane Wiggins looked out the window of her Cedar Rapids office and saw a cloud unlike any she’d seen before. “It looked like Armageddon,” she told the Associated Press. “The shadows of the clouds, the lights and the darks, and the greenish-yellow backdrop. They seemed to change.”
Wiggins sent a photo to the Cloud Appreciation Society, a weather-watching group founded by Gavin Pretor-Pinney, author of The Cloudspotter’s Guide. Other sightings were registered around the world (this one appeared over Tallinn, Estonia), and eventually Pretor-Pinney nominated it as an entirely new type.
The 2017 edition of the World Meteorological Organisation’s International Cloud Atlas included asperitas in a supplementary feature. The name is Latin for “roughen” or “agitate” — “not necessarily gentle or steady, but quite violent-looking, turbulent, almost twisted in its appearance,” Pretor-Pinney said.
It’s not new, really — such clouds have always been up there — but it’s the first formation added to the atlas since 1951. “We like to believe that just about everything that can be seen has been,” Society executive director Paul Hardaker said. “But you do get caught once in a while with the odd, new, interesting thing.”
Yale statistician Frank Anscombe devised this demonstration in 1973. Here are four datasets, each with 11 (x,y) points:
| I | II | III | IV | ||||
|---|---|---|---|---|---|---|---|
| x | y | x | y | x | y | x | y |
| 10.0 | 8.04 | 10.0 | 9.14 | 10.0 | 7.46 | 8.0 | 6.58 |
| 8.0 | 6.95 | 8.0 | 8.14 | 8.0 | 6.77 | 8.0 | 5.76 |
| 13.0 | 7.58 | 13.0 | 8.74 | 13.0 | 12.74 | 8.0 | 7.71 |
| 9.0 | 8.81 | 9.0 | 8.77 | 9.0 | 7.11 | 8.0 | 8.84 |
| 11.0 | 8.33 | 11.0 | 9.26 | 11.0 | 7.81 | 8.0 | 8.47 |
| 14.0 | 9.96 | 14.0 | 8.10 | 14.0 | 8.84 | 8.0 | 7.04 |
| 6.0 | 7.24 | 6.0 | 6.13 | 6.0 | 6.08 | 8.0 | 5.25 |
| 4.0 | 4.26 | 4.0 | 3.10 | 4.0 | 5.39 | 19.0 | 12.50 |
| 12.0 | 10.84 | 12.0 | 9.13 | 12.0 | 8.15 | 8.0 | 5.56 |
| 7.0 | 4.82 | 7.0 | 7.26 | 7.0 | 6.42 | 8.0 | 7.91 |
| 5.0 | 5.68 | 5.0 | 4.74 | 5.0 | 5.73 | 8.0 | 6.89 |
Each set produces the same summary statistics (mean, standard deviation, and correlation). But their graphs are strikingly different:
The lesson, Anscombe said, is to “make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding.”
Justin Matejka and George Fitzmaurice created a similar collection in 2017: the Datasaurus Dozen.
(Thanks, Rick.)
09/05/2021 UPDATE: Here’s an animation of the Datasaurus Dozen. (Thanks, Eric.)
The modern strawberry has a surprisingly dramatic story, involving a French spy in Chile, a perilous ocean voyage, and the unlikely meeting of two botanical expatriates. In this week’s episode of the Futility Closet podcast we’ll describe the improbable origin of one of the world’s most popular fruits.
We’ll also discuss the answers to some of our queries and puzzle over a radioactive engineer.
Certainly rectangular cuboids exist whose edges and face diagonals all have integer lengths.
For example, in 1719 Paul Halcke discovered one with edges (a, b, c) = (44, 117, 240) and face diagonals (d, e, f ) = (125, 244, 267).
But does one exist whose space diagonal (here shown in red) also has integer length?
As of last September, none has been found and no one has proven that none exist.
When a tornado struck Mayfield, Ohio, in 1842, Western Reserve College mathematician Elias Loomis noticed that several fowl had been picked almost clean of their feathers. To find out what wind velocity could accomplish this, he charged a cannon with 5 ounces of gunpowder and inserted a freshly killed chicken in place of a ball:
As the gun was small, it was necessary to press down the chicken with considerable force, by which means it was probably somewhat bruised. The gun was pointed vertically upwards and fired; the feathers rose twenty or thirty feet, and were scattered by the wind. On examination they were found to be pulled out clean, the skin seldom adhering to them. The body was torn into small fragments, only a part of which could be found. The velocity is computed at five hundred feet per second, or three hundred and forty one miles per hour. A fowl, then, forced through the air with this velocity, is torn entirely to pieces; with a less velocity, it is probable most of the feathers might be pulled out without mutilating the body.
“If I could have the use of a suitable gun I would determine this velocity by experiment,” he ended. “It is presumed to be not far from a hundred miles per hour.”
(Elias Loomis, “On a Tornado Which Passed Over Mayfield, Ohio, February 4th, 1842,” American Journal of Science 43:2 [July-September 1842], 278-301.)
