## The Test for the Controlled Variable

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This program demonstrates the test for the controlled variable which is a way to determine what a person is doing on purpose. When you click the "Dodging Donuts" button below a new window will appear with some familiar Simpsons characters moving around the screen. You can pick one of the characters and move it with the mouse so that it dodges (or takes bites of) the on-coming stream of donuts. The character dodging (or nibbling) the donuts is the one you are controlling -- that is, the one you are moving "on purpose". But the mouse moves all three characters at the same time so you could be moving any one of the three character on purpose. And it is impossible to tell, just by looking at the movements of the characters on the screen, which is the one being moved on purpose. The computer is able to figure this out, however, and when it does, tthe character you are moving on purpose become Mr.Burns.At that point you can "change your mind" and purposefully dodge(or eat) donuts with another character. The computer should be able to "read your mind" and figure out which character you are now moving on purpose. Each time the computer detects the character you are moving on purpose you can change to a new character. You can keep doing this, switching arbitrarily from one character to another, to see how well the computer reads your mind.

The computer is able to determine your purpose (to read your mind) by doing a version of the control theory based "test for the controlled variable". The movements of all three characters are potential controlled variables. The computer determines the controlled character (the one moved on purpose) by continuously calculating the correlation between the movements of each character and the disturbance to each character. A different time varying disturbance is applied to each character. In order to keep the movements of the controlled character under control, you have to oppose the effects of the disturbance to that character. This means that the correlation between the character's movement and the disturbance to those movements will be lowest for the controlled square. The correlations between each character's movements and disturbance to its movements can be toggled on and off the display by pressing the mouse button. The lower the correlation (which is the correlation between disturbance and actual mvoements of the character) the more likely the character is controlled (being moved on purpose).