The Brazil Nut Effect

https://commons.wikimedia.org/wiki/File:Mixed_nuts_small_white2.jpg
Image: Wikimedia Commons

When a container of granular material is shaken, we might expect the largest particles to make their way to the bottom. Instead the opposite often happens: Vibrating a container of mixed nuts, muesli, or raisin bran often brings the largest (and presumably heaviest) items to the top.

Precisely why this happens is unclear. An irregularly shaped Brazil nut might “shoulder” its way above smaller nuts as it turns among them; the rising of large particles might help to lower the center of mass of the aggregate; or perhaps the size of the largest particles prevents them from descending in a container’s natural convection flow once they reach the surface. For now it’s an unsolved problem in physics.

| Science & Math

Noted

https://commons.wikimedia.org/wiki/File:Straight_tusked_elephant_Eemian_landscape.jpg
Image: Wikimedia Commons

J.M. Roberts’ 1987 Hutchinson History of the World contains this arresting sentence:

At one site in Spain the mind of what one scholar called a ‘primitive Archimedes’ has been seen at work three hundred thousand years ago, directing the removal and use of the tusks of slaughtered elephants as levers to shift the carcasses for cutting up.

The scholar seems to be archaeologist François Bordes, who had written in his 1968 book The Old Stone Age that the Acheuleans of Torralba-Ambrona had killed elephants half engulfed in mud, “and that a primitive Archimedes had the idea of using their tusks as levers for shifting their enormous bulk and making it easier to cut them up.”

From what I can understand, the evidence for butchery at these sites is now thought to be ambiguous, but it’s a striking image nonetheless.

Completely unrelated, but similarly notable: In Days With Bernard Shaw, his 1948 memoir of his friendship with George Bernard Shaw, Stephen Winsten remembers Shaw remarking, “Leonardo da Vinci ruled his notebooks in columns headed fox, wolf, bear and monkey and made notes of human faces by ticking them off in these columns.” I can’t confirm this either, but it seems worth recording.

| Art · History · Science & Math

Conway’s 99-Graph Problem

https://commons.wikimedia.org/wiki/File:33-duoprism_graph.svg

In this network of 9 points, any two points that are linked have 1 linked point in common, forming a triangle. Any two points that aren’t linked have 2 linked points in common, forming a quadrilateral. Is such a pattern possible in a network of 99 points? In 2014 Princeton mathematician John Horton Conway offered $1000 for the answer to this question; so far the prize is unclaimed.

| Science & Math

Upstream Contamination

This is surprising: When water is poured from one container into another, floating particles can climb upstream, like inanimate salmon, into the higher container. Argentine physicist Sebastian Bianchini first noticed the phenomenon while making tea during his studies at the University of Havana. His paper inspired further work at Rutgers, which has confirmed the effect, but exactly what’s happening isn’t fully understood.

| Science & Math

Juggling

https://math.stackexchange.com/questions/4710716/crazy-fact-about-circles-drawn-on-base-of-triangle-between-cevians-they-alwa/4711623

Take any triangle and divide it into sub-triangles as shown. Inscribe a circle in each of these smaller triangles.

Rearrange the order of the circles and adjust the intervening lines so that each line touches two circles:

https://math.stackexchange.com/questions/4710716/crazy-fact-about-circles-drawn-on-base-of-triangle-between-cevians-they-alwa/4711623

No matter how this is done, each circle will always fit perfectly in its triangle. Here are some proofs.

| Science & Math

Misc

  • The newsletter of the Procrastinators’ Club of America is called Last Month’s Newsletter.
  • Samuel Johnson’s 1755 Dictionary defines dross as “the recrement or despumation of metals.”
  • A sphere of radius n kilometers has almost exactly the same volume as a cube of side n miles. (Randall Munroe)
  • Cookie Monster’s real name is Sid.
  • “Henry James chews more than he bites off.” — Clover Adams

“There exist only two kinds of modern mathematics books: ones which you cannot read beyond the first page and ones which you cannot read beyond the first sentence.” — Physics Nobelist Yang Chen-Ning

| Entertainment · Language · Literature · Quotations · Science & Math · Trivia

Ghost Tint

https://commons.wikimedia.org/wiki/File:Neon_Color_Circle.gif
Image: Wikimedia Commons

There’s no blue circle here. The space among the lines is white. In the presence of black lines, the hue of a colored object seems to bleed into the surrounding background.

The phenomenon was first discovered in 1971. It’s known as neon color spreading.

| Oddities · Science & Math