childhood
A crumpled drawing
A child is walking with a crumpled drawing in his hand. Someone asks him if the crumped drawing has a "name"...
"Every thing," he replies.
If children are transferred from a lively city street
In real life, what significant change does occur if children are transferred from a lively city street to the usual park or to the usual public or project playground?
In most cases (not all, fortunately), the most significant change is this: The children have moved from under the eyes of a high numerical ratio of adults, into a place where the ratio of adults is low or even nil. To think this represents an improvement in city child rearing is pure daydreaming.
Inheriting Froebel's Gifts
A Podcast by Kurt KohlstedtFroebel’s Gifts were meant to be given in a particular order, growing more complex over time and teaching different lessons about shape, structure and perception along the way. A soft knitted ball could be given to a child just six weeks old, followed by a wooden ball and then a cube, illustrating similarities and differences in shapes and materials. Then kids would get a cylinder (which combines elements of both the ball and the cube) and it would blow their little minds. Some objects were pierced by strings or rods so kids could spin them and see how one shapes morphs into another when set into motion. Later came cubes made up of smaller cubes and other hybrids, showing children how parts relate to a whole through deconstruction and reassembly.
These perception-oriented “Gifts” would then give way to construction-oriented “Occupations.” Kids would be told to build things out of materials like paper, string, wire, or little sticks and peas that could be connected and stacked into structures.
Walking lessons
A TweetLecturing Birds on How to Fly, from Nassim Nicholas Taleb's Antifragile
If children started school at six months old and their teachers gave them walking lessons, within a single generation people would come to believe that humans couldn't learn to walk without going to school.
Who Becomes an Inventor in America? The Importance of Exposure to Innovation
A Research PaperWe directly establish the importance of environment by showing that exposure to innovation during childhood has significant causal effects on children's propensities to invent. Children whose families move to a high-innovation area when they are young are more likely to become inventors. These exposure effects are technology-class and gender specific.
Wang tiles
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.