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The card is dropped on this pile. The performer announces that he will cause this single card to travel magically from the left pile to the pile on the right. The left pile is picked up and the cards dealt off by pairs. The pairs come out even, with no card left over. The right hand pile is picked up and the cards taken off by pairs as before.

After all the pairs are dealt, a single card remains! Method: The working is due to the fact that there are seven pairs of cards. When these pairs are separated, each pile will contain seven cards—an odd number. Adding the extra card, therefore, makes this an even pile.

If the cards are dealt by pairs, without counting them aloud, no one will notice that one pile contains one more pair than the other. This trick is at least fifty years old. It is known as "The Piano Trick" because the position of the spectator's hands suggests playing a piano. The performer asks someone to cut a small packet of cards from the deck.

He then cuts a larger packet for himself. The magician counts his cards. We will assume he has twenty. He now announces, "I have as many cards as you have, plus four cards, and enough left to make Let us say he has eleven. The magician deals his cards to the table, counting up to eleven. He then places four cards aside, according to his statement, and continues dealing, counting 12, 13, 14, 15, The sixteenth card is the last one, as he predicted.

The trick is repeated over and over, though the prediction varies each time in the number of cards to be placed aside—sometimes three, sometimes five, and so on.

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It seems impossible for the magician to make his prediction without knowing the number of cards taken by the spectator. Method: It is not necessary for the performer to know the number held by the spectator. He simply makes sure that he takes more cards than the other person.

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He counts his cards. In the example given, he has twenty. He then arbitrarily picks a small number such as 4, subtracting it from 20 to get The statement is worded, "I have as many cards as you have, plus four extra cards, and enough left to make sixteen. The method of counting seems to involve the spectator's number, though actually the magician is simply counting his own cards, with the exception of the four which are placed aside.

Varying the number to be set aside each time serves to impress the spectator with the fact that somehow the formula is dependent on the number of cards he is holding. A deck of cards is shuffled by the audience. The magician places it in his pocket and asks someone to call out any card that comes to mind. For example, the Queen of Spades is named.

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He reaches into his pocket and removes a spade. This, he explains, indicates the suit of the chosen card. He then removes a four and an eight which together total 12, the numerical value of the queen. He places these four cards in his pocket, remembering their order. The shuffled pack is later placed in the pocket beneath these four cards so that they become the top cards of the pack. The audience, of course, is not aware of the fact that four cards are in the magician's pocket while the deck is being shuffled.

Because the four cards are in a doubling series, each value twice the previous one, it is possible to combine them in various ways to produce any desired total from 1 to Moreover, each suit is represented by a card. The card with the appropriate suit is removed from the pocket first.

If this card is also involved in the combination of cards used to give the desired total, then the additional card or cards are removed and the values of all the cards are added.

Mathematics, Magic and Mystery by Martin Gardner

Otherwise, the first card is tossed aside and the card or cards totaling the desired number are then taken from the pocket. As we shall see in later chapters, the doubling principle involved in this trick is one that is used in many other mathematical magic effects. Occasionally one of the four cards will be named.

In this case the magician takes the card itself from his pocket—a seeming miracle! A spectator shuffles the deck and places it on the table. The magician writes the name of a card on a piece of paper and places it face down without letting anyone see what has been written. And every now and then, I'm discovering a new bit of it. That's exactly what it feels like. But is that just a feeling? Could it be that mathematics is purely a product of the human brain?

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Using f. That's characteristic of lots of math-gifted types.

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But is that the result of teaching, and intense practice, or are the foundations of math built into our brains? Scientists are looking for the answer here, at the Duke University Lemur Center, a acre sanctuary in North Carolina, the largest one for rare and endangered lemurs, in the world. Like all primates, lemurs are related to humans through a common ancestor that lived as many as million years ago. Scientists believe lemurs share many characteristics with those earliest primates, making them a window, though a blurry one, into our ancient past. What are all of these different animals doing when they compare two quantities?

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Well, clearly he's not using verbal labels, he's not using symbols. We need to figure out whether they can really use number, pure number, as a cue. The red square starts a round.

If he touches it, two squares appear, containing different numbers of objects. He's been trained that if he chooses the box with the fewest number, he'll get a reward, a sugar pellet. She has conducted thousands of trials and shown that lemurs and rhesus monkeys can learn to pick the right answer.

So, is he counting, is he doing what a human child does when they recite the numbers, one, two, three? And yet, what he seems to be attending to is the very abstract essence of what a number is. Rats, pigeons, fish, raccoons, insects, horses and elephants all show sensitivity to quantity. And so do human infants. At her lab on the Duke campus, Liz has tested babies that were only six months old.

They'll look longer at a screen with a changing number of objects, as long as the change is obvious enough to capture their attention. Liz has also tested college students, asking them not to count but to respond as quickly as they could to a touch screen test comparing quantities. The results? About the same as lemurs and rhesus monkeys. LIZ BRANNON: In fact, there are humans who aren't as good as our monkeys, and others that are far better, so there's a lot of variability in human performance, but, in general, it looks very similar to a monkey.

Even without any mathematical education, even without learning any number words or symbols, we would still have, all of us, as humans, a primitive number sense. That fundamental ability to perceive number seems to be a very important foundation, and without it, it's very questionable as to whether we could ever appreciate symbolic mathematics. NARRATOR: The building blocks of mathematics may be preprogrammed into our brains, part of the basic toolkit for survival, like our ability to recognize patterns and shapes or our sense of time.

From that point of view, on this foundation, we've erected one of the greatest inventions of human culture: mathematics. But the mystery remains. Through science, technology and engineering, it's transformed the planet, even allowing us to go into the beyond. Their work depended on a groundbreaking discovery, from the Renaissance, that turned mathematics into the language of science: the law of falling bodies.

The ancient Greek philosopher Aristotle taught that heavier objects fall faster than lighter ones. An idea that, on the surface, makes sense, even this surface: the Mars yard, where they test the rovers at J. Well, we're not in Pisa, we don't have cannon balls, but we do have a bowling ball and a bouncy ball. Let's weigh them.

First, we weigh the bowling ball. It weighs 15 pounds. And the bouncy ball, it weighs hardly anything.

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This isn't that high though. Maybe we should drop them from higher.