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

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Discussion Overview

The discussion explores the differences between Zeno's paradox and the Thompson lamp, focusing on the concept of "supertasks" in mathematics and philosophy. Participants examine the characteristics that define supertasks and consider examples, including the bouncing ball, to understand their implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants define a supertask as a task that requires an infinite number of tasks, noting that Zeno's paradox may only superficially qualify as a supertask due to its finite sum.
  • Others suggest that certain tasks, like divergent series, represent true supertasks that are impossible to complete.
  • A participant questions whether a bouncing ball could be considered a supertask, prompting further exploration of its characteristics.
  • Another participant argues that while all motion could qualify as a supertask in principle, specific scenarios, such as a bouncing ball that reduces height by a factor, do not meet the criteria due to requiring infinite time.

Areas of Agreement / Disagreement

Participants express differing views on what qualifies as a supertask, with no consensus reached on the characteristics that define them or the applicability of examples like the bouncing ball.

Contextual Notes

Definitions of actions and operations in the context of supertasks are noted as important, but the discussion remains open-ended regarding the specific criteria for identifying supertasks.

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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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.
 
Would a bouncing ball be considered a candidate for a supertask?
 
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?
 
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.
 

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