Zeno's Paradox of Motion:Thompson's Lamp Scenario

In summary: Like the switch that turns the lamp on and off, each motion seems to be followed by an opposite motion. But in the end, the lamp is either on, or off. In summary, the paradox of THOMPSON'S LAMP explores the idea of infinite time intervals and whether or not they can add up to a finite amount of time. The question of whether the lamp will be on or off after two minutes is a matter of perspective, as it depends on whether the starting state was on or off. However, from a mathematical standpoint, the sequence does not have a limit and the alternating series does not converge, leading to the conclusion that the state after two minutes cannot be determined despite having complete information about the previous times.
  • #1
BlindBeauty
9
0
This question is probably so easy that I'm making it too complicated but here it is:

"THOMPSON'S LAMP: Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. Applying the above discussion, it is easy to see that all these infinitely many time intervals add up to exactly two minutes."

"QUESTION: At the end of two minutes, is the lamp on, or off?"

Conceptually, without mathematical background, I would say ON since it was ON when it began. But why? Why not? Mathematically?

"ANOTHER QUESTION: Here the lamp started out being off. Would it have made any difference if it had started out being on?"

Again, conceptually, I would say yes, it would be ON if it started ON. But what's the answer? Mathematically?

Thanks.
David
 
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  • #2
I don't think it will matter. The question of being on or off is related to the number of switches, i.e. if it's an even or odd number of switches.
When you take the limit for the number of switches to infinity (and hence get the result that it will take 2 minutes), the information of odd or even is lost, it can be both.
 
  • #3
Since this is a math question, not really a physics question, I'll be moving this to a more appropriate forum. This issue is: Does the inifinite series (1 - 1 + 1 - 1 ...) converge? I'd say no.
 
  • #4
That's another why of looking at it, but don't you mean the sequence 1,-1,1,-1,... (where 1 represents on and -1 represents off, for example)?
Either way, the sequence doesn't have a limit and the (alternating) series doesn't converge in this case.
 
  • #5
It isn't a maths question, at least it isn't a non-vacuous maths question. Parity is a property of finite sets not infinite ones.

Just because someone thinks they have a well formed question doesn't mean they do. I think you'd've been better off deleting the question entirely, not moving it to maths. I doubt anybody here wants it.
 
  • #6
I agree with matt that this doesn't belong in math -- I believe the main point of this paradox is to deal with the issues of modelling reality. I guess philosophy of math & science is the best fit, so I'll toss it over there.

Making some implicit assumptions explicit, the paradox goes like this:

Assumption: it is really possible for a physical situation to behave as stated in the problem.
Fact: knowing everything about a system before a certain time allows you to determine the state of the system at that time.
Paradox: the state after two minutes cannot be determined, despite the complete information of the previous times!
 
  • #7
Thanks. I WAS making it too complicated!
 
  • #8
This sounds tangential to me.
As there is a definite limited block of time to work within, the switching would have to get progressively faster and faster the closer it drew to the two min mark, in a seemingly tangential fashion. Always closer but never reaching, achieving greater than light speed, double light speed, quad, etc. Given the parameters of the problem, it sounds like a fallacious problem on the face. By the 'end' of two min, the light would appear, for all intents and purposes, continuous.
Like 'motion' and 'time'.
 

What is Zeno's Paradox of Motion?

Zeno's Paradox of Motion is a philosophical problem created by Greek philosopher Zeno of Elea in the 5th century BC. It proposes that motion is impossible because in order to reach a certain distance, one must first travel half that distance, and then half of the remaining distance, and so on infinitely. This paradox challenges our understanding of the concept of motion and has been a topic of debate for centuries.

What is Thompson's Lamp Scenario?

Thompson's Lamp Scenario is a modern version of Zeno's Paradox of Motion, created by philosopher James Thompson in the 1950s. It involves a lamp that is switched on for one minute, then switched off for half a minute, then switched on for a quarter of a minute, and so on infinitely. This paradox raises questions about the nature of time and whether it can be divided infinitely.

How does Zeno's Paradox of Motion challenge our understanding of the physical world?

Zeno's Paradox of Motion challenges our understanding of the physical world by proposing that motion is impossible. It suggests that the concept of motion, which is fundamental to our understanding of the universe, may actually be an illusion. This paradox has led to many debates and discussions among philosophers and scientists about the nature of reality and the concept of infinity.

What are some proposed solutions to Zeno's Paradox of Motion?

There have been many proposed solutions to Zeno's Paradox of Motion throughout history. Some philosophers and scientists suggest that the paradox is based on a flawed understanding of the concept of infinity and can be solved by using mathematical concepts such as limits. Others propose that Zeno's Paradox is a thought experiment and does not have a real-world application. Ultimately, there is no universally accepted solution to this paradox.

How does Thompson's Lamp Scenario relate to Zeno's Paradox of Motion?

Thompson's Lamp Scenario is a modern version of Zeno's Paradox of Motion and raises similar questions about the nature of time and motion. It highlights the paradoxical nature of dividing time and distance into infinitely small parts, and challenges our understanding of these concepts. While Thompson's Lamp Scenario may offer a different perspective on the paradox, it ultimately adds to the ongoing discussion and debate surrounding Zeno's Paradox of Motion.

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