Grass Hoppers

George and May Southgate patented these rather alarming “jumping shoes” in 1922. Each is a giant replica of Schistocerca americana made of spring steel and secured by a strap over a child’s shoe.

“He will spring or jump much farther than he would be able to without our improved device; and furthermore, the shock upon the system when alighting will be greatly reduced, thus enabling the user to cover considerable ground with a minimum effort.”

This will all end in litigation, but in the meantime “the flapping of the wings will greatly increase the enjoyment of the users.”

November 20, 2013November 19, 2013 | Technology

Tree Mountain

http://www.flickr.com/photos/amymyou/518300581/ — Image: Flickr

Twenty years ago, 11,000 people planted 11,000 trees on an artificial mountain near Ylöjärvi, Finland. The trees were planted in a mathematical pattern based on the golden section; in time they will grow into a virgin forest each tree of which has a designated custodian. The trees can change ownership, but they can never be removed from the forest, and the mountain itself can never be owned or sold.

Artist Agnes Denes conceived the project in 1982, and the Finnish government undertook it 10 years later. The site is legally protected for the next 400 years.

November 20, 2013November 19, 2013 | Art

Lifeboats for All

In 1993, I attended a technology and art conference, ‘Ars Electronica,’ in Linz, Austria, where my former postdoctoral student Pattie Maes gave a talk titled ‘Why Immortality Is a Dead Idea.’ She took as many people as she could find who had publicly predicted downloading of consciousness into silicon, and plotted the dates of their predictions, along with when they themselves would turn seventy years old. Not too surprisingly, the years matched up for each of them. Three score and ten years from their individual births, technology would be ripe for them to download their consciousness into a computer. Just in the nick of time! They were each, in their own minds, going to be remarkably lucky, to be in just the right place at the right time.

— MIT roboticist Rodney Brooks, Flesh and Machines, 2003

November 20, 2013November 19, 2013 | Technology

The Halkett Boat

Royal Navy officer Peter Halkett designed this lightweight “boat cloak” in 1844. When deflated, its hull could be worn as a cloak, the oar used as a walking stick, and the sail as an umbrella, but a portable bellows could inflate it in four minutes into a craft that could carry eight people.

Explorer John Richardson, who had nearly died of hypothermia trying to cross an arctic river during John Franklin’s disastrous Coppermine Expedition of 1819, wrote that “Had we been possessed of such a contrivance in our first expedition, I have little doubt of our having brought the whole party in safely.” But the navy saw no use for Halkett’s boats, and his efforts to promote them to outdoorsmen similarly failed. The two remaining specimens reside in museums.

November 19, 2013November 18, 2013 | Technology

“On a Certain Scholar”

He never completed his History of Ephesus,
But his name got mentioned in numerous prefaces.

— W. Craddle

November 19, 2013November 18, 2013 | Poems

Bootstrap Percolation

grid infection puzzle

On a 12 × 12 grid, some squares are infected and some are healthy. On each turn, a healthy square becomes infected if it has two or more infected orthogonal neighbors. (In the example above, the black squares are infected, the white squares are healthy, and the gray squares will be infected next turn.) What’s the smallest number of initially infected squares that can spread an infection over the whole board?

	Select Click for Answer
Twelve (or, on an n × n grid, n). The key is to notice that the total perimeter of the infected area never increases. Since the fully infected board has a perimeter of 48, we need an initial arrangement of infected squares with a perimeter of at least 48, or 48/4 = 12 squares. The simplest example is a long diagonal. From Béla Bollobás, The Art of Mathematics, 2006.

November 19, 2013November 29, 2013 | Puzzles

“When a Man’s Busy”

When a man’s busy, why, leisure
Strikes him as wonderful pleasure:
‘Faith, and at leisure once is he?
Straightway he wants to be busy.

— Robert Browning

November 18, 2013November 17, 2013 | Poems

Naturally

Steven Bartlett and Peter Suber’s Self-Reference: Reflections on Reflexivity contains a bibliography of works on reflexivity.

It includes an entry for Steven Bartlett and Peter Suber’s Self-Reference: Reflections on Reflexivity.

November 18, 2013November 17, 2013 | Science & Math

Unquote

“Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed.” — Albert Einstein

“When we observe nature, and especially the ordering of nature, it is always ourselves alone we are observing.” — G.C. Lichtenberg

November 18, 2013November 17, 2013 | Quotations

Counterfeit Redux

A more challenging version of the Counterfeit Coin puzzle from 2011:

You have 12 coins, one of which has been replaced with a counterfeit. The false coin differs in weight from the true ones, but you don’t know whether it’s heavier or lighter. How can find it using three weighings in a pan balance?

	Select Click for Answer
Put four coins in each pan. If they balance, then all these coins are good. Weigh three of them against three of the four remaining unknown coins. If they balance then the remaining untested coin is bad; if not then we’ve identified three suspected-bad coins and we’ve discovered whether the counterfeit coin is heavy or light. Weighing two of the three suspected coins against one another will reveal the bad one. If the first weighing does not balance, then the four untested coins are good and we have four suspected-heavy coins and four suspected-light ones. Call these three groups G, H, and L. In the second weighing, put HHHL in the left pan and HGGG in the right: If the left pan sinks, then one of its suspected-heavy coins is a heavy counterfeit, and we can find it by trying to balance two of the three, as above. If the right pan sinks, then the culprit is either the suspected-light coin in the left pan or the suspected-heavy one in the right pan. To decide between them, weigh one of these against a known-good coin in the third weighing. If the two pans balance, then the bad coin is one of the three suspected-light coins that are presently off the scale. Weighing two of these against one another will identify the bad coin, as above.

Click for Answer

November 17, 2013November 22, 2013 | Puzzles