Thomson's Lamp Paradox

Intro and Statement

In this article, we are going to look at a paradox put forth by the British philosopher James F. Thomson. The thought experiment is meant to be an example of something that has both an infinite number of tasks and can complete in a finite amount of time. (Thomson dubbed this a “supertask”). So the experiment goes like this: You turn on a lamp and set a timer for 2 minutes. After 1 minute, you turn the lamp off. You wait another 30 seconds and then turn the lamp on. Wait 15 seconds and turn the lamp off again. And you continue this process of flipping the switch whenever the time remaining cuts in half. Your timer will go off after 2 minutes—that much is guaranteed. However, when the timer does go off, will your lamp be on or off? 🤔

Python to the Rescue

Instead of taking a measured, philosophical approach and coming up with a definitive answer to this question, I think it’s more fun to just let Python take the reins and answer it for us (kind of). We’ll have to introduce a threshold value for this to be practical, but we won’t worry about that too much because it’s already not exactly like the “true” experiment. The “true” experiment would require completely instant switching and instant and perfectly precise measurement of the remaining time. In any case, we can still have fun with our Python implementation!

We can just be object-oriented about this and first define a Lamp class. It can be on or off, so we’ll represent that as a Boolean class member. And the only other thing we need is a method for flipping the switch. In practice, you just simply represent the lamp as a Boolean, but it may be more descriptive to write it this way.

# lamp.py
import time # We'll need this later

class Lamp:
    on = True

    def __init__(self, on=True):
        self.on = on

    def hit_switch(self):
        self.on = not self.on

So we have a Lamp class that we can instantiate in our experiment function. Now let’s code the rest of it.

def lamp_experiment() -> bool:
    lamp = Lamp(on=True)
    duration = 120 # seconds
    current_time = time.time()
    last_time_switched = current_time
    end_of_timeout = current_time + duration
    while end_of_timeout - time.time() > 0:
        if ((end_of_timeout + last_time_switched) / 2 - current_time) < threshold:
            lamp.hit_switch()
            last_time_switched = time.time()
        current_time = time.time()
    return lamp.on
# Don't forget to call the method
print(lamp_experiment())

The main idea here is that we have to get the midpoint of the last time the light was toggled and the end time. When the current time is approximately equal to that midpoint, we hit the switch again. Now let’s run it.

python3 lamp.py

Lamp Simulator

Or if you’d like to see how this goes in JS…

Results and Conclusion

So, is the lamp on or off?

Regardless of your answer, it still doesn’t really answer Thomson’s question, but it is definitely a fun exercise. And it’s cool to translate a thought experiment into code. In any case, hope you found this to be interesting and let me know if you’d like to see any other thought experiments answered by Python!