| | Ed, thanks for the reply. On the matter of sleight-of-hand, it is complicated.
First, you the audience must be old enough for "object permanence." If hiding behind your hands makes the world go away, stage magic lacks a metaphysical foundation for you.
Culturally, you have to know that rabbits do not live in hats. In the 19th century, when people who lived on farms came into the city, and saw a stage magician, they had an experiential awareness of rabbits. Bugs Bunny was the only rabbit in my life, though I guess I understood that they were small animals like dogs or bigger than birds. Pouring milk into a paper cone is another. You have to know what a funnel is and have made one. By six or so, you do that.
As for the mentalist routines, the one you mention is, indeed, a basic arithmetic trick. When I was in junior high, our weekly science magazine explained it. Then we could all play the game. Years and years later, I bought my daughter the trick, a little wand of four glittery colors that has nothing to do the actual working of it.
As for the New Age arithmetic, it was not that the earlier mode was "anti-conceptual" but ony that our experience is now more abstract than the the older ways. We have more experience and we can teach children other ways to calculate, from arithmetic to calculus, we stand on the shoulders of giants.
Again, decimal arithmetic as we know it only goes back to 1650 or so. The German thaler was divided into thirds and fourths to make 12ths and only was supplanted after unification in 1871. Arabic numerals made adding and subtracting much easier. Long division still required complicated learning. But it was better than Roman numerals. As if anyone ever actually needed to divide 841 by 33.
That could have been a complaint by a "conservative" parent of 1500 who knew Roman numerals and saw no need for the new math.
What we know as the checkerboard was used for counting stacks of coins. It is why the British government Treasury department was called the Exchequer. The "new age" methods taught today are only a paper-and-pencil way to move and group the stacks.
Mostly, common measures were ways to group things pints, quarts, gallons, hogsheads, ... inches, feet, rods, furlongs... pence, shillings, pounds: 240 pennyweights to the pound. Everyone knows that (or did at one time). American merchants along the East Coast kept their books in pounds-shilling-pence into the 1830s. Even today, two bits is a quarter, though we no longer use the 8-bit Spanish dollar in daily trade. The 8-bit Spanish dollar was customary in the United States until 1857. These American bank notes show Spanish money as their promises to pay in US money. (Website home page here.)
The problem with the dime was that it was not half of a quarter dollar. The 20-cent piece of the 1870s was an attempt to fix that. Mostly, people used debased Spanish coins called "pistereens" to stand for 12-1/2 cents. Here is a picture of a saloon token from 1900 from Alaska for 6-1/4 cents: four of them make a quarter dollar.
A hundred years ago, as the "high school movement" was being launched a "conservative" could have complained that important traditional knowledge about how to divide a dollar was no longer being taught by the public schools.
I mention all this here because conservative anti-individualism is a reflection of conservative anti-intellectualism. Which is the chicken and which is the egg? Whatever the Tea Party Parent learned as a child is for them God's Commandment. They hold up ancient Rome (or Judaea) as a standard and complain that individualism is a symptom of the breakdown in society. They are not culturally or intellectually in the Renaissance - and not at all ready for the second renaissance and the rebirth of reason.
(Edited by Michael E. Marotta on 10/20, 8:01am)
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