What is the difference between Zeno's paradox and the Thompson lamp?

In summary, the conversation discusses the concept of supertasks and how they involve an infinite number of tasks being completed in a finite amount of time. Examples such as Zeno's paradox and the Thompson lamp are mentioned, with the goal of determining which supertasks are possible and which are not. It is noted that the bouncing ball problem, while involving an infinite number of tasks, is not a true supertask as it requires an infinite amount of time to complete. The article linked in the conversation is suggested as a further resource for understanding supertasks.
  • #1
quantumdude
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What is the difference between Zeno's paradox and the Thompson lamp?

In PF v2.0, Ontoplasma brought this up, and I thought it was worth having a look at. Let's go through some of these "supertasks" together.

http://plato.stanford.edu/entries/spacetime-supertasks
 
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  • #2
[inte]?
 
  • #3
Ben,

Check out the link. It gives a concise definition of a supertask. In brief, it is a task that requires (or appears to require) an infinite number of tasks. Some of them (such as Zeno's paradox) are only superficially "supertasks" due to the fact that the infinite series has a finite sum. Others are represented by divergent series, and are thus truly impossible.

The aim of this thread is to find a way to determine which are possible and which are not. The solution to the problem is mathematical, which is why I posted it here.

I'll have more later.
 
  • #4
Would a bouncing ball be considered a candidate for a supertask?
 
  • #5
I don't quite see why not. But then, I'm not very sure...are there specific characteristics(or tricks) that help with identifying supertasks?
 
  • #6
Supertask defined:
"A supertask is an infinite sequence of actions or operations carried out in a finite interval of time."

The writer is also careful about his definitions of action and operation, as they do not necessarily require the action of a person.

But on to the immediate question:

Oringinally posted by Ben-CS:
Would a bouncing ball be considered a candidate for a supertask?

Depends. In principle, all motion qualifies, a la Zeno. However, if you are talking about the bouncing ball problem in which the ball rises to a height that is reduced by a factor r after each bounce and showing that it travels a finite distance, then no, that is not a supertask, as it requires an infinite amount of time.

If you're still interested, print out the article I linked you to in the first post, and let's have a look at it.
 

1. What is Zeno's paradox?

Zeno's paradox is a philosophical puzzle that was created by the ancient Greek philosopher Zeno of Elea. It consists of a series of paradoxical statements and arguments that challenge our understanding of motion and change.

2. What is the Thompson lamp paradox?

The Thompson lamp paradox is a modern variation of Zeno's paradox that was proposed by J.F. Thompson in 1954. It involves a lamp that is switched on and off in a series of intervals, each half the length of the previous one, resulting in an infinite number of switches in a finite amount of time.

3. What is the main difference between Zeno's paradox and the Thompson lamp?

The main difference between Zeno's paradox and the Thompson lamp is their origin and context. Zeno's paradox was created in ancient Greece and was used to challenge the concept of motion and change, while the Thompson lamp paradox was proposed in modern times as a thought experiment to explore the nature of infinite processes.

4. How do Zeno's paradox and the Thompson lamp relate to each other?

Zeno's paradox and the Thompson lamp are both based on the concept of infinite processes and challenge our understanding of time, motion, and change. The Thompson lamp can be seen as a variation or modern interpretation of Zeno's paradox, using a similar concept to explore philosophical questions.

5. What is the significance of Zeno's paradox and the Thompson lamp?

Zeno's paradox and the Thompson lamp have both played important roles in the development of philosophy and mathematics. They have sparked debates and discussions about the nature of time, infinity, and motion, and have influenced the thinking of many philosophers and scientists throughout history.

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