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The Thomson Lamp
Suppose you have a lamp with a simple
on/off switch. Press the switch when it is off and the lamp will be
turned on, press it again and it will be turned off. Now suppose you
run the following experiment. You turn the lamp on at the start of
a minute. Thirty seconds later, you turn it off. In another fifteen
seconds, you turn it back on, then 7 1/2 seconds later back off again,
and so on throughout the midpoints of whatever time remains. Now the
question is this. At the end of the minute, will the lamp be on or
off?
Since the lamp has been turned on and off an infinite number of times,
for every time it has been turned on, it has been turned off, and
vice versa. At the end of the minute, therefore, it can be neither
on nor off. But it must be one or the other.
Attempts to find fault in this paradox often attack
some irrelevant aspect of the argument. Thus one sometimes hears the
criticism that this situation is physically impossible, since no mechanism
could operate indefinitely fast. The on/off switch would not be able
to keep up. As a counter argument to this type of criticism, I offer
the following simplified version of the Thomson Lamp
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