Froebel’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.
A Fermi estimate is a quick-and-dirty solution to an arbitrary scientific or engineering analysis problem. Fermi estimation uses widely known numbers, readily observable phenomenology, basic physics equations, and a bunch of approximation techniques to arrive at rough answers that tend to be correct within an order of magnitude or so. The term is named for Enrico Fermi, who was famously good at this sort of thing.
…It struck me that there is counterpart to this kind of thinking on the synthesis side, where you use similar techniques to arrive at a very rough design for a complex engineered artifact. I call such a design approach Dyson design, after the physicist Freeman Dyson, who was one of the best practitioners of it (not to be confused with inventor James Dyson, whose designs, ironically, are not Dyson designs).