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.”

Tree Mountain

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.

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

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.

“On a Certain Scholar”

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

— W. Craddle

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?

Click for Answer

“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


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.


“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

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?

Click for Answer