# Another infinity question **URL:** \ **Category:** Factual Questions\ **Created:** [June 6, 2003, 10:46pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190 "2003-06-06T22:46:20Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 7, 2003, 12:52pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/21 "2003-06-07T12:52:18Z")
> [@](#): > > \*Originally posted by Phnord Prephect \* > \*\*Well, first off, the statement “, it is easy to see that all these infinitely many time intervals add up to exactly two minutes.” is intentionally misleading. It does not. > > There is such a thing as a time quanta. An indivisible unit of time, the shortest possible duration. I don’t know what this is offhand. It is incredibly small. > > Therefore, one cannot divide beyond this point. When the genie reaches a single chronon (??) or fraction thereof, that’s it. He’s done. It doesn’t continue indefinitely. > > So therefore, all ya gotta do is the math… 1 second, plus 1/2, plus 1/4, plus 1/8… plus one chronon, and it’s over. One presumes he waits the tiny fraction of a second that remains, to make two full seconds, at this point. > > Then just count the clicks. q;} \*\* There is no such thing as time quanta, you are probably thinking of Planck time (I’ve seen people call it a quanta of time, but it is not). As far as has been obsreved time is continous and not discrete. I have heard people _propose_ that time is divided up into quanta of time called chronons there is no observational evidence to suggest they are. ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 7, 2003, 10:46pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/22 "2003-06-07T22:46:43Z")
[hijack] I was under the impression that the Planck time _was_ a ‘quanta of time’ in that the idea of any unit of time less than the Planck time was meaningless… **MC** any chance of you going into a little more detail as to your logic? My knowledge comes from my reading on String Theory, where the idea of minimum lengths of time/length etc. are pretty important. And besides, if there is a universal speed limit (speed of light, c) and a minimum unit of length (Planck length Lp, universally accepted I think…) then surely the ratio **Lp/c** gives a minimum unit of time? Or is this logic back to front? Nevertheless, time needs to be measured and any unit of time less than the ‘minimum unit’ I just defined would be immeasurable wouldn’t it? [/hijack] ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [June 7, 2003, 11:01pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/23 "2003-06-07T23:01:57Z")
The basic problem is that the Planck units are merely scales on which we know that a classical description of gravity is going to fail utterly and totally, in the same way as, for example, the Bohr radius is a scale on which we can’t really do classical physics anymore. Same basic idea: we combine the relevant fundamental constants and come up with a size scale that gives us a rule of thumb for when something funny is going to be happening. What exactly that “something funny” is, we couldn’t tell you. The string theorists think they have a theory which could explain it, and if they’re right, then perhaps the odd concept of duality would make the Planck length the shortest meaningful distance, and perhaps not. Regardless, it is certainly not the case that we have any proof that length comes in precise quanta of the Planck length, and most physicists out there would say, in fact, that this is because it isn’t the case to begin with. Analagously, the Planck time is a timescale on which classical gravity is not going to work at all, but it is not the shortest possible amount of time. ---
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 7, 2003, 11:19pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/24 "2003-06-07T23:19:46Z")
Planck Time is the time that Quatum gravity takes over from classical gravity, not necessarily an indivisble unit. There’s no experimental evidence to suggest that time is quantized and there is certainly evidence to suggest that the Planck Time cannot be an indivisble unit of time: [http://www.astronomy.com/Content/Dynamic/Articles/000/000/001/219fcvov.asp](http://www.astronomy.com/Content/Dynamic/Articles/000/000/001/219fcvov.asp) (also it should be noted as the article is misleading in this way, that quantum physics doesn’t treat time as a state variable but a co-ordinate postion) ---
**Author:** ![eburacum45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum45/32/8690_2.png) [@eburacum45](https://boards.straightdope.com/u/eburacum45)\ **Post date:** [June 7, 2003, 11:29pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/25 "2003-06-07T23:29:38Z")
ooh does that mean that the Planck length is not the smallest possible length too? Xeno was right. * * * SF worldbuilding at [http://www.orionsarm.com/main.html](http://www.orionsarm.com/main.html) ---
**Author:** ![zwaldd](https://avatars.discourse-cdn.com/v4/letter/z/a9adbd/32.png) [@zwaldd](https://boards.straightdope.com/u/zwaldd)\ **Post date:** [June 7, 2003, 11:32pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/26 "2003-06-07T23:32:42Z")
The demon (he’d have to be, right?) would vanish. The lamp…or at least the parts moving during all this… would vanish as well. For the demon to perform this task infinitely, time would have to stop relative to him. For the lamp to be capable of such manipulation, time would have to stop for it. What happens to something for which time stops, relative to us, the observers? I would think the thing would cease to exist. If it lacks the fourth dimension, duration, it’s just not there anymore. ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 7, 2003, 11:32pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/27 "2003-06-07T23:32:54Z")
Thanks for clearing that up guys; this kinda stuff hasn’t really come my way yet (although next year there are a coupla courses on my timetable that look like they may go into the subject), I’m far too busy trying to pass 2nd year maths and physics to worry about things not on the exams! ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 7, 2003, 11:35pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/28 "2003-06-07T23:35:01Z")
**zwaldd** , it’s a _thought experiment_; things like physics don’t come into it because it’s just a scenerio to help the reader think about a particular mathematical process; it’s abstract. ---
**Author:** ![zwaldd](https://avatars.discourse-cdn.com/v4/letter/z/a9adbd/32.png) [@zwaldd](https://boards.straightdope.com/u/zwaldd)\ **Post date:** [June 7, 2003, 11:47pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/29 "2003-06-07T23:47:13Z")
> [@](#): > > \*Originally posted by green\_dragon \* > \*\ ***zwaldd** , it’s a _thought experiment_ \*\* I thought about it! ---
**Author:** ![zwaldd](https://avatars.discourse-cdn.com/v4/letter/z/a9adbd/32.png) [@zwaldd](https://boards.straightdope.com/u/zwaldd)\ **Post date:** [June 8, 2003, 12:06am UTC](https://boards.straightdope.com/t/another-infinity-question/180190/30 "2003-06-08T00:06:12Z")
> [@](#): > > \*Originally posted by green\_dragon \* > **at two minutes he has stopped switching the switch in the way the question describes.** I don’t think so…he never stops switching the switch. To him, the switching goes on for ever. The remaining existence of this being occurs in the moment leading up to two minutes. The moment beyond two minutes is infinitely beyond his reach. ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 8, 2003, 1:22am UTC](https://boards.straightdope.com/t/another-infinity-question/180190/31 "2003-06-08T01:22:40Z")
Well _yes_ but it’s a practical way of describing something which is, in fact, abstract…if you want to talk time dilation etc. then that’s a subject for another thread! If it helps I can rephrase the question in mathematical terms… ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 8, 2003, 1:28am UTC](https://boards.straightdope.com/t/another-infinity-question/180190/32 "2003-06-08T01:28:22Z")
In any reasonable mathematical sense, the state of the light after two minutes is undefined. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [June 9, 2003, 10:20pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/33 "2003-06-09T22:20:45Z")
So, no dopers out there can tell me how an infinite amount of actions can be performed in a finite amount of time? ---
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 9, 2003, 10:24pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/34 "2003-06-09T22:24:07Z")
You can’t perform infinite amount of actions of equal value in a finite time, the paradox itself is evidence for this. ---
**Author:** ![Logical\_Phallacy](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Logical\_Phallacy](https://boards.straightdope.com/u/Logical_Phallacy)\ **Post date:** [June 9, 2003, 10:25pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/35 "2003-06-09T22:25:34Z")
why does no one bother to take into account the physical limmits of the lamp/hand? Or the size of the foot relative to the wall in xeno’s paradox? wouldn’t that solve the problem? ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 9, 2003, 10:27pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/36 "2003-06-09T22:27:13Z")
I thought I addressed that in my first post, but here goes again: You _can’t_…there are physical limitations (like you’d have to be moving faster than lightspeed after a while)…in a mathematical, abstract sense, well, have a look at my first post, the one about the number line, and now imagine that the line is just part of a clock, and that’s what’s happening. Happy? ---
**Author:** ![MC\_Master\_of\_Ceremonies](https://avatars.discourse-cdn.com/v4/letter/m/bb73d2/32.png) [@MC\_Master\_of\_Ceremonies](https://boards.straightdope.com/u/MC_Master_of_Ceremonies)\ **Post date:** [June 9, 2003, 10:31pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/37 "2003-06-09T22:31:00Z")
Because the physical limits are undefined as it’s an abstract problem. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [June 9, 2003, 10:42pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/38 "2003-06-09T22:42:51Z")
**Green\_dragon** , aren’t you the one who had to remind another poster that this is a thought question, and the laws of physics don’t apply? But just for the hell of it, this being is all powerful, and can move faster than the speed of light. He can constantly switch the switch in half the time as the last. Has the switch moving after two minutes? ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [June 9, 2003, 10:44pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/39 "2003-06-09T22:44:42Z")
Correction: Has the switch stopped moving after two minutes? ---
**Author:** ![green\_dragon\_1](https://avatars.discourse-cdn.com/v4/letter/g/13edae/32.png) [@green\_dragon\_1](https://boards.straightdope.com/u/green_dragon_1)\ **Post date:** [June 9, 2003, 10:58pm UTC](https://boards.straightdope.com/t/another-infinity-question/180190/40 "2003-06-09T22:58:37Z")
> [@](#): > > \*Originally posted by x-ray vision \* > \*\ ***Green\_dragon** , aren’t you the one who had to remind another poster that this is a thought question, and the laws of physics don’t apply? \*\* Yep, but if we’re talking about ‘how to do infinite things in a finite amount of time’, a discussion of physical limitations is bound to crop up. If the guy can move faster than the speed of light, well, time will reverse direction for him so in fact he’ll never get to 2 minutes:D Oh? But what if we ignore that? Well, if you ignore enough physics you’re basically just doing abstract maths so we’re back to square 1. [Previous page](https://boards.straightdope.com/t/another-infinity-question/180190.md?page=1) [Next page](https://boards.straightdope.com/t/another-infinity-question/180190.md?page=3)