Organ Function Grinder

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Visitors have a choice of 24 different input numbers, each printed on a paper ticket with a bar code. The visitor picks one ticket, and sets three separate dials on the front of the "organ function grinder". Once the visitor has set the three dials, he or she turns a hand crank on the front to start the organ function grinder.

The three dials are each labeled with these 8 functions:

  • add three
  • subtract three
  • double
  • halve
  • square
  • extract square root
  • leave alone
  • invert (1/x)

The ticket value is the input for the first function, set by the first dial, and each output becomes the input for the next function. The final output is printed on a special ruler (see below), which comes out the other side of the organ function grinder. On the ruler are printed the original input, the overall function, and the final output.

Organ Function Grinder

The sandwich board will display a target number. The visitor should be told to try to set the dials so that the output number equals the target. You can mentally work out with them how the input will be transformed, to help them see if their choice of functions will be close to the target. After they then turn the crank and get their output, see if it is correct. After the goal is reached, you can pick a new goal number and post it. One way to choose a new number is to have someone spin the Universal Wheel of Chance, but check to make sure the number is attainable.

The output is printed on a special eight-inch ruler with only a few markings. There is not a mark for every inch, but you can still measure any whole number of inches from 1 to 8 using the available marks. You can point this out to them and challenge them to design similar rulers for 12 inches or other lengths, using as few marks as possible.

The music that plays when the crank is turned is mathematically transformed along with the input number. You can point out to visitors that the input determines a simple melody. If the function adds three to the input, the melody goes up. If it subtracts three, the melody goes down. If the function doubles or halves, the melody speeds up or slows down. If they invert, the melody inverts (high notes become low and vice versa).

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Organ Function Grinder
Organ Function Grinder