Suppose you decide that you’ll walk (at 3 mph) to any destination that’s within a mile of your house, and bike (at 15 mph) to any destination that’s farther away. That’s a reasonable choice, but it has a surprising result: You’ll actually arrive more quickly at moderately distant points (1 to 5 miles away) than at most points closer to home (less than 1 mile away).

Psychologist Daniel Gilbert uses this example to illustrate a phenomenon in our reactions to stressful events: Sometimes we’ll recover more quickly from particularly distressing experiences because they’re strong enough to invoke defense processes that attentuate stress.

Since its launch in 1991, arXiv, Cornell’s open-access repository of electronic preprints, has cataloged more than 2 million scientific papers.

In 2010, Caltech physicist David Simmons-Duffin created snarXiv, a random generator that produces titles and abstracts of imaginary articles in theoretical high-energy physics. Then he challenged visitors to distinguish real titles from fake ones.

After 6 months and 750,000 guesses in more than 50,000 games played in 67 countries, “the results are clear,” he concluded. “Science sounds like gobbledygook.” On average, players had guessed right only 59 percent of the time. Real papers most often judged to be fake:

• “Highlights of the Theory,” by B.Z. Kopeliovich and R. Peschanski
• “Heterotic on Half-Flat,” by Sebastien Gurrieri, Andre Lukas, and Andrei Micu
• “Relativistic Confinement of Neutral Fermions With a Trigonometric Tangent Potential,” by Luis B. Castro and Antonio S. de Castro
• “Toric Kahler Metrics and AdS_5 in Ring-Like Co-ordinates,” by Bobby S. Acharya, Suresh Govindarajan, and Chethan N. Gowdigere
• “Aspects of U_A(1) Breaking in the Nambu and Jona-Lasinio Model,” by Alexander A. Osipov, Brigitte Hiller, Veronique Bernard, and Alex H. Blin
• “Energy’s and Amplitudes’ Positivity,” by Alberto Nicolis, Riccardo Rattazzi, and Enrico Trincherini

Try it yourself.

While we’re at it: SCIgen randomly generates research papers in computer science, complete with graphs, figures, and citations; and Mathgen generates professional-looking mathematics papers, with theorems, proofs, equations, discussion, and references.

(Via Andrew May, Fake Physics: Spoofs, Hoaxes and Fictitious Science, 2019.)

Mathematikum, the science museum in Giessen, Germany, contains this clever device for multiplying pairs of numbers. The parabola presents the curve y = x². Now suppose we want to multiply 10 by 9. We find the points -10 and 9 on the x axis, follow them up to the curve, and hang a weighted string over the pegs that we find there. The string crosses the y axis at (0, 90), so 10 × 9 = 90.

A simulator, and an explanation of the principle, are here.

Another remarkable contribution by Lee Sallows:

(Thanks, Lee!)

If Chicken McNuggets come in packs of 6, 9, and 20, what’s the largest number of McNuggets that you can’t buy?

Steve Omohundro and Peter Blicher posed this question in MIT Technology Review in May 2002, and Ken Rosato contributed a neat solution.

The answer is 43. To start, notice that we can use the 6-packs and 9-packs to piece together any multiple of 3 other than 3 itself. 43 itself is not divisible by 3, so 6-packs and 9-packs alone won’t get us there, and adding some 20-packs won’t help, since we’d have to add them to a quantity of either 23 or 3, neither of which can be assembled from packs of other sizes. So that shows that 43 itself can’t be reached.

But we still need to show that every larger number can be. Well, we can create all the larger even numbers by adding some quantity of 6-packs to either 36, 38, or 40, and each of those foundations can be assembled from the packs we have (36 = 9 + 9 + 9 + 9, 38 = 20 + 9 + 9, and 40 = 20 + 20). So that takes care of the even numbers. And adding 9 to any of these even numbers will give us any desired odd number above 43, starting with 36 + 9 = 45.

So 43 is the largest number of Chicken McNuggets that can’t be formed by combining 6-packs, 9-packs, and 20-packs.

(I think Henri Picciotto was the first to broach this arresting question, in Games magazine in 1987. Since then, McNuggets have found their way into Happy Meals in 4-piece servings, reducing the largest non–McNugget number to 11. In some countries, though, the 9-piece allotment has been increased to 10 — and in that case there is no largest such number, as no odd quantity can ever be assembled.)

In their 1981 book Facts and Fallacies, Chris Morgan and David Langford note that the biblical reference to the “four corners of the earth” would apply equally well if the world were a tetrahedron.

In a similar spirit, as American airman Joseph Portney was flying over the North Pole in 1968 he wondered, “What if the Earth were … ?” He made sketches of 12 fanciful alternate Earths and gave them to Litton’s Guidance & Control Systems graphic arts group, which created models that were featured in the company’s Pilots and Navigators Calendar of 1969. This made an international sensation, and Portney’s creations were subsequently published for use in classrooms worldwide, inviting students to ponder what life would be like on a cone or a dodecahedron.

Portney graduated from the U.S. Naval Academy and went on to work for Litton on high-altitude navigation problems — for example, designing control systems that could guide an aircraft around one of these strange worlds.

The Internet Archive has the whole complement.