Are supertasks impossible?

...is the essay question I've stupidly decided on for my paradoxes class. I've got 3000 words and it's designed with a philosophical bent, but the philosophy encyclopedia I'm looking at goes into a fair amount of detail about the physics side and touches on the maths. I'm probably going to go into detail about the maths a bit more than the physics, but I know a lot of the .org are pretty damned good when it comes to knowledge about science and whatnot.

So what do you guys think? Supertasks- possible or impossible?

Conrad (it's been a slow day for me today, you may have noticed)

[Mr Speirs]

errrr whats a supertask??? Would be my answer. Supertask isn't a word in the dictionary.

A supertask may be defined as an infinite sequence of actions or operations carried out in a finite interval of time. - from the stamford encyclopedia of philosophy.

Thompson's lamp is probably the best example of this, from wikipedia:


Thomson's lamp is a puzzle that is a variation on Zeno's paradoxes. It was devised by philosopher James F. Thomson, who also coined the term supertask.
Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose a being able to perform the following task: starting a timer, he turns the lamp on. At the end of one minute, he turns it off. At the end of another half minute, he turns it on again. At the end of another quarter of a minute, he turns it off. At the next eighth of a minute, he turns it on again, and he continues thus, flicking the switch each time after waiting exactly one-half the time he waited before flicking it previously. The sum of all these progressively smaller times is exactly two minutes.
The following questions are then considered:

• Is the lamp on or off after exactly two minutes?
• Is the lamp switch on or off after exactly two minutes?
• Would it make any difference if the lamp had started out being on, instead of off?

I think you would blow the bulb like that.

Um - there is no spoon.

Okay, imagine it as a desmodroic valve-type system that when one closes the other opens, only they each open at half the time it took for the last opening- it opens at 60 seconds, 30 seconds, 15 seconds etc.

Is one valve open or closed after 2 minutes?

If there is a finite amount of time it takes to do the switching, then the lamp will be either on or off when it gets to a timed two minutes. If it is a theoritical switch that can swith instantaneously, then I have no idea. You could semi sum it up by saying it is calculable if the time taken to do the switching (even if miniscule) is longer than the smaller possible unit of time. If time can be divided up into infinite time also, then you will iterate to two but never get there. But actually that has reminded me that actually 0.9999999 recurring has actually been proven to be 1 somehow.


So yeah, I have no idea, sorry

A difficult question.

First, from wikipedia, a definition:

"In philosophy, a supertask is a task occurring within a finite interval of time involving infinitely many steps (subtasks)"

The most common analogy then being movment - to get from step A to step B, there are many movements...one must first get to halfway, and before that halfway of halfway...and so on. It has been argued that no-one then really moves and therefore movemtn is impossible. But thats twaddle, we can all move pretty easily!

Dividing up events into such infinitesimal tasks is similar to the idea of quantum theory - it all falls apart at the macroscopic level. There are some materials (quantum dots i think) that, at a certain number of atoms, behave like a single atom. Raise the amont of atoms in the dot by a few more (say 10) and the quantum dot looses its quantum-ness. Thinks are still occuring in a quantum manner at some level, but not at the observable level...

Originally Posted by Warthog

I think you would blow the bulb like that.

That's not so silly an answer as you might think:

bla bla science physics etc infinite time regression etc ...and will thereby bring about an electrical short-circuit that will make all the current in the generator pass through the cable on which the switch is set, leaving nothing for the more resistant path where the lamp...

Due to kinematics.

Maybe at 2 minutes both states are true? Like atoms can be in two places at the same time, that has also been proven I think.