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(Message started by: srn347 on Aug 30th, 2007, 10:07am)
Title: supertasks
Post by srn347 on Aug 30th, 2007, 10:07am
Zeus gathers an infinite amount of demons and gives the following demands: demon 1 kill prometheus in an hour, demon 2 kill him in half an hour, demon 3 kill him in a quarter of an hour...
Prometheus was found dead in that hour. Zeus was taken to court. Why was he found innocent? You get the next supertask riddle after solving this one.
Title: Re: supertasks
Post by Archae on Sep 1st, 2007, 8:19am
I would say, to answer this 'supertask', that Zeus was found innocent because he could argue that there is no way that a demon could have killed Prometheus.
Assume that all demons act in the same manner  - they either all obey Zeus or all disobey him.  If the latter is the case, it is clear to see that Prometheus' death was not caused by Zeus at all.  In the former case, Zeus can argue that no demon killed Prometheus: if you assign blame to a certain demon, then Zeus can show that the next demon he created would have killed Prometheus first, so the demon accused could not have done it.  And since he created an infinite amount of these demons, there is no first demon who killed Prometheus.

However, Zeus should still be charged for premeditated murder.
Title: Re: supertasks
Post by srn347 on Sep 1st, 2007, 9:45am
Correct. Next supertask. There is a hotel with an infinite amount of people. If its full, how do you fit another person? Or another infinite amount of people? Or another infinite amount of infinite amounts of people?
Title: Re: supertasks
Post by denis on Sep 1st, 2007, 3:33pm
See the link below....

http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1180160232;start=20#20

Note that if you can check another person into the hotel, then you can't really say the hotel is full. By definition, full means there is no vacancy and that you can't fit in anymore people.
Title: Re: supertasks
Post by srn347 on Sep 1st, 2007, 4:02pm
Correct. Next supertask. There is a light that is on. A person turns the switch off in a minute, on in 30 seconds, off in 15 seconds...
In 2 minutes(which he will be done by that time), will the light be on or off and will the switch be on or off(at that speed, the light might not keep up with the switch)?
Title: Re: supertasks
Post by denis on Sep 1st, 2007, 4:51pm
The light will be off because the switch will be broken from overuse ;)
Title: Re: supertasks
Post by srn347 on Sep 1st, 2007, 7:16pm
Good answer, but no.
Title: Re: supertasks
Post by mikedagr8 on Sep 2nd, 2007, 5:27am
You can't tell, as you near the two minutes, you will be going so fast, that it wont change. So I'll go with on. By what I have said, I mean that 1/2+1/4+1/8+.... never actually reaches 1.

Do these puzzles have something in common? They seem to have so far.
Title: Re: supertasks
Post by denis on Sep 2nd, 2007, 7:00am
Supposing the switch is still working, we won't know what position it's in at the two minute mark because if you say it's on, there exists a time interval (half of the last time interval used to set it to on) whereby it will be set to off. If you say it's off, there exists a time interval (half of the last time interval used to set it to off) whereby it will be set to on.  So you really can't tell.

Whether  the light is on or off in 2 minutes depends on the type of lamp. I think, an incandescant bulb would have its filament still hot enough to emit a sufficient amount of light to be considered on (but dimmer than regular on). A fluorescent light would probably be off because its latency time to turn on exceeds the intervals times between the quick on/off switching near the 2 minute mark.
Title: Re: supertasks
Post by srn347 on Sep 2nd, 2007, 8:09am
Should I just give you the answer?
Title: Re: supertasks
Post by denis on Sep 2nd, 2007, 8:14am

on 09/02/07 at 08:09:33, srn347 wrote:
Should I just give you the answer?



That's really up to you but generally, you give a little bit of time for others to chime in with their answers or give hints.
Title: Re: supertasks
Post by srn347 on Sep 2nd, 2007, 10:10am
Ok. The light switch won't break or anything like that.
Title: Re: supertasks
Post by Archae on Sep 3rd, 2007, 10:41pm
Well, unless I am misreading the question, it should be off, along with the switch in the 'off' position.  Reread the problem:

on 09/01/07 at 16:02:24, srn347 wrote:
There is a light that is on. A person turns the switch off in a minute, on in 30 seconds, off in 15 seconds...
In 2 minutes(which he will be done by that time), will the light be on or off and will the switch be on or off(at that speed, the light might not keep up with the switch)?

The way I interpret the riddle, we start at time t=0 and proceed to two minutes (t=2).  By the rules, at t=1/4, the light will be off; at t=1/2, the light will be on; at t=1, the light will be off again.
Pretty much, what's happening here is that the infinite series is constructed to be approaching the two minute mark, but when the flicking actually occurs in practice, that order will be reversed.  Then the problem of running off to infinity occurs in the millisecond (and smaller) right after the clock starts, and in another instant, we do not need to worry about it anymore.  Then, the last flick will be at t=1, which will turn the switch and the light off, and will stay like that until t=2.  (Unless, of course, there is another flick precisely at t=2, in which case - which seems more true as I write it - that light should be on.)

But, if I have completely misinterpreted the question, I would say that the light should be both on and off simultaneously, so the position of the switch is both correct and incorrect.

Just my two cents.
Title: Re: supertasks
Post by srn347 on Sep 4th, 2007, 8:51pm
Misenterpretation. Maybe I should give the answer after one more close guess.
Title: Re: supertasks
Post by Whiskey Tango Foxtrot on Sep 5th, 2007, 11:13am
I also think this is a trick involving the order in which you stated the actions.  By stating them backwards you made us think the light is first modified after a minute, then again after thirty seconds, etc.  In reality, the first change takes place after an infinitesimally small amount of time.  The changes continue taking place until fifteen seconds, when the light is turned off.  It is turned on at thirty seconds, back off at the one minute mark, and will be turned on at two minutes.

I'm pretty sure this is what Archae was saying but I found it a bit confusing on the first read-through.
Title: Re: supertasks
Post by srn347 on Sep 5th, 2007, 4:47pm
That's the same answer as stated(incorrectly) previously.
Title: Re: supertasks
Post by Whiskey Tango Foxtrot on Sep 5th, 2007, 6:26pm
Okay, then I say it will be off.  The reasoning is the same as above except there is no switching at the 2 minute mark.
Title: Re: supertasks
Post by Archae on Sep 5th, 2007, 7:29pm
Sorry for the poor wording, there.  I was kinda rambling on I realize (saying things as they hit me), so it didn't make much sense.
I'll keep on the problem.
Title: Re: supertasks
Post by srn347 on Sep 5th, 2007, 10:59pm
It will be off, but not why you said. If a switch is in the middle(which it will be), the light will be off. And for the next one, a machine can in half an hour make a machine half its size, but twice as fast. In an hour, how many will there be? What size(in terms of the original machines size)?
Title: Re: supertasks
Post by towr on Sep 6th, 2007, 12:21am

on 09/05/07 at 22:59:21, srn347 wrote:
If a switch is in the middle(which it will be)
No it won't.
Just try it ;)

(Mathematically speaking its state is undefined; not in the middle. And physically, it's impossible.)
Title: Re: supertasks
Post by SMQ on Sep 6th, 2007, 7:46am

on 09/05/07 at 22:59:21, srn347 wrote:
a machine can in half an hour make a machine half its size, but twice as fast. In an hour, how many will there be? What size(in terms of the original machines size)?

"Just before" an hour there will be a countable infinity of machines: one of each size 1, 1/2, 1/4, 1/8, etc.  "Just after" an hour there will be a countable infinity of machines, but "almost twice as many": one of size 1 and two each of sizes 1/2, 1/4, 1/8, etc.  (The terms in quotes are not rigorously defined in the reals, but could be with hyperreals.)

The first machine makes a machine of 1/2 size at 1/2 hour and at 1 hour.  The second machine makes a machine of 1/4 size as 3/4 hours and at 1 hour.  The third machine makes a machine of 1/8 size at 7/8 hours and at 1 hour, etc.

--SMQ
Title: Re: supertasks
Post by srn347 on Sep 6th, 2007, 4:19pm
I have tried it, have you?
Title: Re: supertasks
Post by Archae on Sep 6th, 2007, 11:01pm
It depends on the switch I believe: I have had switches that will stay in the middle with the light off, but also switches that will rest in the middle with the light on.
Title: Re: supertasks
Post by JiNbOtAk on Sep 7th, 2007, 1:51am

on 09/06/07 at 00:21:17, towr wrote:
(Mathematically speaking its state is undefined; not in the middle. And physically, it's impossible.)


I think what towr meant is that switches are discrete, it can only be either on, or off. To say that the switch in the middle position, from between on and off, would result in the bulb being turned on ( or off ), is pointless, as that would mean the on ( or off ) position would just need to be shifted to the current middle position. ( Am I making any sense ? )

Anyway, if switches aren't discrete, one would expect it to act like dimmers, where the middle position would cause the bulb to still be on, but the light is somewhat dimmer.
Title: Re: supertasks
Post by towr on Sep 7th, 2007, 2:47am
No, what I meant was that physically toggling a switch with infinite speeds makes it go back in time; trying to accelerate it to an infinite speed increases its mass to the point you form a black hole; also once it reached light speed, time for the switch stops and it can't go faster; and even at much lower speeds the switch will already be destroyed due to internal material stresses. ::)

And mathematically speaking the end state is indeterminate. It's equivalent to asking "is the last natural number odd or even", ignoring that there is no such number.
Title: Re: supertasks
Post by JiNbOtAk on Sep 7th, 2007, 3:18am

on 09/07/07 at 02:47:12, towr wrote:
No, what I meant was that physically toggling a switch with infinite speeds makes it go back in time; trying to accelerate it to an infinite speed increases its mass to the point you form a black hole; also once it reached light speed, time for the switch stops and it can't go faster; and even at much lower speeds the switch will already be destroyed due to internal material stresses. ::)

And mathematically speaking the end state is indeterminate. It's equivalent to asking "is the last natural number odd or even", ignoring that there is no such number.


Oh, never mind then.  :P
Title: Re: supertasks
Post by srn347 on Sep 7th, 2007, 4:24pm
Actually, it's more like asking if infinity is odd or even and getting that it might not be an integer since it's barely a real number.
Title: Re: supertasks
Post by mikedagr8 on Sep 8th, 2007, 2:05am

on 09/07/07 at 16:24:05, srn347 wrote:
Actually, it's more like asking if infinity is odd or even and getting that it might not be an integer since it's barely a real number.


Listen, seriously now. If you don't know, don't say, as TB's title states or similar...

Infinity is not a real number. Simple proof. Domains and ranges are written with either an '(' or '[' as an opening bracket or ')' ']'. The circular one means not including and the other, including. INFINITY ALWAYS HAS A CIRCULAR BRACKET!!!
Title: Re: supertasks
Post by srn347 on Sep 8th, 2007, 8:04am
That is irelevant. I have already asked the next supertask riddle.
Title: Re: supertasks
Post by SMQ on Sep 8th, 2007, 8:11am
And I've already answered it.  [text removed for spring cleaning]

--SMQ
Title: Re: supertasks
Post by srn347 on Sep 8th, 2007, 11:55am
You haven't said how much space in terms of the first machine they will take up total.
Title: Re: supertasks
Post by SMQ on Sep 8th, 2007, 12:48pm
I gave the siszes of the individual machines; from there it's just a matter of summation: "just before" an hour the assembled machines will have total size 2.  "just after" an hour they will have total size 3.

--SMQ
Title: Re: supertasks
Post by srn347 on Sep 8th, 2007, 2:31pm
Ok. Next supertask. A person tries to run a mile, but an infinite amount of gods try to stop him. If he runs half a mile, the first one paralysis him, if he runs a quarter mile, the second one paralysis him, etc. When does he get paralysed?
Title: Re: supertasks
Post by Whiskey Tango Foxtrot on Sep 9th, 2007, 8:22am
I think we all have a decent understanding of limits now.  We do not require another carbon-copy "supertask."
Title: Re: supertasks
Post by srn347 on Sep 9th, 2007, 10:15am
If you all have an understanding of it, one of you answer it.
Title: Re: supertasks
Post by towr on Sep 9th, 2007, 10:42am

on 09/09/07 at 10:15:30, srn347 wrote:
If you all have an understanding of it, one of you answer it.
Why? You don't have an understanding of it and won't accept the right answer when we give it. What's the point then?
Title: Re: supertasks
Post by srn347 on Sep 9th, 2007, 11:45am
We won't know that until someone answers.
Title: Re: supertasks
Post by towr on Sep 9th, 2007, 12:14pm
Oh, we know. We learn from experience.
Title: Re: supertasks
Post by srn347 on Sep 9th, 2007, 6:53pm
Then why don't we see any answers?
Title: Re: supertasks
Post by SMQ on Sep 9th, 2007, 7:10pm
OK, I'll bite: he is paralyzed as soon as he moves a distance of 1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/varaleph.gif0 toward his goal.

--SMQ
Title: Re: supertasks
Post by srn347 on Sep 9th, 2007, 7:15pm
A number, I need a number.
Title: Re: supertasks
Post by towr on Sep 10th, 2007, 12:08am

on 09/09/07 at 19:15:05, srn347 wrote:
A number, I need a number.
That was a number; see what I mean, there's no point.
Title: Re: supertasks
Post by Grimbal on Sep 10th, 2007, 12:44am
Let's see: "If he runs half a mile, the first one paralysis him, if he runs a quarter mile, the second one paralysis him, etc." it follows logically that if he runs 0 mile the third one paralyzes him and if he runs -1/4 mile, the fourth one paralyzes him.  So a possible answer is that he gets paralyzed on the spot by deity #3.
Title: Re: supertasks
Post by Noke Lieu on Sep 10th, 2007, 12:45am
What a curious situation we seem to be in.
I've tried to resist posting about this quandry, but I guess I finally caved.

I am surprised that it has taken as long as it has to attract such a character. It's been close a couple of times-
by no means is srn347 alone in their unwaivering obstinance, undiminishable sense of self-importance and ability to promote a sense of disharmony. Anyone remember the godfathers that were here a year or two ago? They come, they go.

In essence, and I remember saying the following about another blackguard that was frequenting this venerable site a while back (and equally using it as a source of puerile entertainment for themselves by constipating our somewhat cerebral musings)

They're intimidated by us, and we don't care about them. Good enough for me.

Doubtless, srn347 is bound to retort in some witless manner, presumably using shadowing, underlining and italics (congratualtions on mastering that, but between you and me- it's just hard to read rather than looking authoratitve)

The problem with arguing with many students is they're too self-obsessed to realise that they're bettered, and end up performing to an audience. So it wouldn't surprise me in the slightest if snr347
is some highschooler boasting to their friend(s) how irritated they gets us.

The irony is that individually, I don't care about this person. I am not irritated by their behaviour, more disappointed. [hide](offending remark)[/hide]

so, to put it blunty srn347 we don't care. we don't care.
We want to be able to care about you, but we don't care.
You're not signifcant enough (really, we don't care)in our daily lives for us to invest (we don't care) any emotion in you.
We don't care.

Your current attitude and lack of respect to us further consolidates our intellectual apathy towards you.

I realise that there seems very little point in asking you to disist with your current course of action, but I implore you to at least consider it.

Goodbye snr347, we shall not converse. (monologues aren't conversations)

Offending remark removed (Grimbal)
Title: Re: supertasks
Post by srn347 on Sep 11th, 2007, 4:57pm
He does get paralyzed at 0 mile, but not by the third one. He gets paralyzed by the last one(not that there is a last one).
Title: Re: supertasks
Post by JiNbOtAk on Sep 11th, 2007, 7:19pm

on 09/10/07 at 00:45:05, Noke Lieu wrote:
(offending remark)


;D

Offending remark removed (Grimbal)
Title: Re: supertasks
Post by srn347 on Sep 13th, 2007, 9:48pm
With those comments, I don't know how people have the odasity to say I'm a spammer instead of you people.
Title: Re: supertasks
Post by JiNbOtAk on Sep 14th, 2007, 1:06am

on 09/13/07 at 21:48:15, srn347 wrote:
With those comments, I don't know how people have the odasity to say I'm a spammer instead of you people.


Odasity ? Don't you mean obesity ? Or maybe opacity ? Perhaps edacity ? English being your first languange, I know for sure you didn't mean audacity..  ;D
Title: Re: supertasks
Post by mikedagr8 on Sep 14th, 2007, 1:14am
More conclusive proof, he is not a "writer".
Title: Re: supertasks
Post by srn347 on Sep 14th, 2007, 7:21pm
Odasity, look it up.
Title: Re: supertasks
Post by towr on Sep 16th, 2007, 8:43am

on 09/14/07 at 19:21:53, srn347 wrote:
Odasity, look it up.

http://dictionary.reference.com/search?q=Odasity
doesn't exist
http://m-w.com/dictionary/Odasity
doesn't exist
http://en.wikipedia.org/wiki/Special:Search?search=Odasity
for some reason gives lists of asteroids..?!
http://en.wiktionary.org/wiki/Special:Search?search=Odasity
doesn't exist.
http://dict.die.net/?q=Odasity
doesn't exist.

Any other dictionaries you could suggest to look up this 'word' in?
Or is it perhaps time to revise the spelling..?
Title: Re: supertasks
Post by Sameer on Sep 16th, 2007, 12:31pm
Here's a superdupertask for everyone!! How do we improve srn347?  ;)
Title: Re: supertasks
Post by towr on Sep 16th, 2007, 12:42pm
Maybe the way you improve wine, lay it in a rack in the cellar, rotate it every day, and hope it improves with age.
Title: Re: supertasks
Post by srn347 on Sep 16th, 2007, 3:58pm
Spammers! Anyway, perhaps odacity is the correct spelling of it. Here's an ultratask for you to do: quit spamming!
Title: Re: supertasks
Post by ima1trkpny on Sep 16th, 2007, 9:53pm

on 09/16/07 at 15:58:18, srn347 wrote:
Spammers! Anyway, perhaps odacity is the correct spelling of it. Here's an ultratask for you to do: quit spamming!

LOL... JiNbOtAk had the correct spelling... it is "audacity"... I find it infinitely amusing that even in your attempted insults you are incapable of presenting a coherent thought or argument... next time if you really can't be bothered learning correct spelling at least go to the trouble of copying and pasting into a word document so spell check can save our eyes from the most offensive of your errors.
Title: Re: supertasks
Post by towr on Sep 16th, 2007, 11:30pm
Firefox 2 has a built-in spell checker. Really convenient.
Title: Re: supertasks
Post by srn347 on Sep 17th, 2007, 6:36am
They already have firefox 2! I have firefox 1.
Title: Re: supertasks
Post by towr on Sep 17th, 2007, 7:51am

on 09/17/07 at 06:36:40, srn347 wrote:
They already have firefox 2! I have firefox 1.
There's even a Firefox 3, but they stopped supporting 1.x (only critical updates), so I upgraded to 2.x; I haven't regretted it.
Title: Re: supertasks
Post by srn347 on Sep 17th, 2007, 6:05pm
Have they invented vista 2?
Title: Re: supertasks
Post by thecow135 on Sep 22nd, 2007, 8:54pm
theyre past vista 2... vista 5.31 just came out... incidently 5-31 is my BDAY WOOT
Title: Re: supertasks
Post by srn347 on Sep 22nd, 2007, 10:08pm
Really? Anyway, time for another supertask. Anyway, you all know the infinite hotel thing I assume. How do you fill it with infinity squared people(each group of infinite people in one of the infinite buses). There are at least two answers.
Title: Re: supertasks
Post by Grimbal on Sep 23rd, 2007, 5:59am
Well, since a countable infinity squared is not more than a countable infinity, you can just apply the same trick.

Method 1:
- Move all hotel guests from room n to room 2n.
- Fill in the odd rooms by starting with passenger 1 from group 1, then p. 2 from g. 1 and p. 1 from g. 2, then passengers such that their number in the group plus group number is 4, then 5, etc.  Each passenger will eventually be placed in a room.

Method 2:
Move hotel guests from rooms pin to rooms pi2n, where {pi} are the prime numbers.
Move guest j of bus i into room pi2j-1
Title: Re: supertasks
Post by srn347 on Sep 23rd, 2007, 4:56pm
Correct. now what about an infinite amount of infinite amounts of infinite amounts of people? or what about an uncountably infinite amount of people.
Title: Re: supertasks
Post by mikedagr8 on Sep 23rd, 2007, 11:50pm
What about stopping these stupid puzzles?
Title: Re: supertasks
Post by Grimbal on Sep 24th, 2007, 12:49am
A (countably) infinite number of (countably) infinite number is a (countably) infinite number.
An uncountably infinite number of people won't fit in a countably infinite number of rooms.


on 09/23/07 at 16:56:27, srn347 wrote:
Correct.

I know.
Title: Re: supertasks
Post by srn347 on Sep 24th, 2007, 7:19pm
An uncountable amount will fit. The countably infinite amount of countably infinite amounts of countably infinite people requires more creativity and the uncountably infinite amount will fit. If it didn't, I wouldn't have asked it.
Title: Re: supertasks
Post by Grimbal on Sep 25th, 2007, 1:19am
What do you mean by uncountably infinite amount?

And are we talking about the aleph-0 hotel?
Title: Re: supertasks
Post by towr on Sep 25th, 2007, 1:31am

on 09/24/07 at 19:19:34, srn347 wrote:
the uncountably infinite amount will fit. If it didn't, I wouldn't have asked it.
Sure you would, because you think you know more about how infinity works than you actually do.
Title: Re: supertasks
Post by srn347 on Sep 25th, 2007, 7:57pm
I know that uncountable infinity is higher than countable infinity, but so is countably infinite squared and it fits.
Title: Re: supertasks
Post by towr on Sep 25th, 2007, 11:34pm

on 09/25/07 at 19:57:50, srn347 wrote:
I know that uncountable infinity is higher than countable infinity, but so is countably infinite squared and it fits.
Countably infinite squared fits because it isn't greater than countably infinite. There is a one to one mapping possible from one to the other. For uncountably infinite that is not the case; and without such a mapping, you can't allocate all the guests to a room.
Title: Re: supertasks
Post by srn347 on Sep 26th, 2007, 7:43pm
Solve the countable infinity cubed and I'll at anyones request explain how to fit an uncountable infinity in it.


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